"Siphonaptera" is a name used[1] to refer to the following rhyme by Augustus De Morgan (Siphonaptera being the biological order to which fleas belong):
Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.[2]
The rhyme appears in De Morgan's A Budget of Paradoxes (1872) along with a discussion of the possibilities that all particles may be made of clustered smaller particles, "and so down, for ever", and that planets and stars may be particles of some larger universe, "and so up, for ever".[2]
The lines derive[3] from part of Jonathan Swift's long satirical poem "On Poetry: A Rapsody" of 1733:
The Vermin only teaze and pinch
Their Foes superior by an Inch.
So, Nat'ralists observe, a Flea
Hath smaller Fleas that on him prey,
And these have smaller yet to bite 'em,
And so proceed ad infinitum:
Thus ev'ry Poet, in his Kind
Is bit by him that comes behind[.][4]
Lewis Fry Richardson adapted the poem to meteorology in 1922:[5]